Answer
Given,
Average speed of Malcolm and Ravi = 260 km/h
Let speed of the Malcolm be X and speed of the Ravi Y.
From the given statement
....(i)
....(ii)
Adding both the equations
3 X = 600
X = 200 km/h
Putting value in equation (i)
Y = 520 - 200
Y = 320 Km/h
Speed of Malcolm = 200 Km/h
Speed of Ravi = 320 Km/h
Answer:
The International Astronomical Union (IAU) downgraded the status of Pluto to that of a dwarf planet because it did not meet the three criteria the IAU uses to define a full-sized planet. Essentially Pluto meets all the criteria except one—it “has not cleared its neighboring region of other objects
Explanation:
Answer:
The tension in the left side string = 17.21 N
The tension in the right side string = F = 27.3 N
Explanation:
Given that
F= 27.3 N
M= 1.43 kg ,r= 0.0792 m
Moment of inertia of disk ,I = 0.5 m r²
I = 0.5 x 1.43 x 0.0792² = 0.0044 kg.m²
m= 0.7 kg
Lets take linear acceleration of system is a m/s²
Lets take tension in left side string = T
From Newtons law
T- mg = ma
T- 0.7 x 10 = 0.7 a ----------1
(F - T) r = I α
α = Angular acceleration of disk
a = α r
(F - T) r = I α
(F - T) r² = I a
( 27.3 - T) x 0.0792² = 0.0044 a --------2
Form equation 1 and 2
a= 1.42 T - 10 m/s²
a = 1.42 ( 27.3 - T) m/s²
1.42 T - 10 = 38.9 - 1.42 T
T=17.21 N
The tension in the right side string = F = 27.3 N
The answer is 35 minutes
The Newton's law of cooling is:
T(x) = Ta + (To - Ta)e⁻ⁿˣ
T(x) - the temperature of the coffee at time x
Ta - the ambient temperature
To - the initial temperature
n - constant
step 1. Calculate constant k:
We have:
T(x) = 200°F
x = 10 min
Ta = 68°F
To = 210°F
n = ?
T(x) = Ta + (To - Ta)e⁻ⁿˣ
200 = 68 + (210 - 68)e⁻ⁿ*¹⁰
200 = 68 + 142 * e⁻¹⁰ⁿ
200 - 68 = 142 * e⁻¹⁰ⁿ
132 = 142 * e⁻¹⁰ⁿ
e⁻¹⁰ⁿ = 132/142
e⁻¹⁰ⁿ = 0.93
Logarithm both sides with natural logarithm:
ln(e⁻¹⁰ⁿ) = ln(0.93)
-10n * ln(e) = -0.07
-10n * 1 = - 0.07
-10n = -0.07
n = -0.07 / - 10
n = 0.007
Step 2. Calculate time x when T(x) = 180°F:
We have:
T(x) = 180°F
x = ?
Ta = 68°F
To = 210°F
n = 0.007
T(x) = Ta + (To - Ta)e⁻ⁿˣ
180 = 68 + (210 - 68)e⁻⁰.⁰⁰⁷*ˣ
180 - 68 = 142 * e⁻⁰.⁰⁰⁷*ˣ
112 = 142 * e⁻⁰.⁰⁰⁷⁾*ˣ
e⁻⁰.⁰⁰⁷*ˣ = 112/142
e⁻⁰.⁰⁰⁷*ˣ = 0.79
Logarithm both sides with natural logarithm:
ln(e⁻⁰.⁰⁰⁷*ˣ) = ln(0.79)
-0.007x * ln(e) = -0.24
-0.007x * 1 = -0.24
-0.007x = -0.24
x = -0.24 / -0.007
x ≈ 35
